Hello everyone,
‘‘Austin Roberts believes that the mean price of houses in the area is greater than $145,000. A random sample of 36 houses in the area has a mean price of $149,750. The population standard deviation is $24,000, and Roberts wants to conduct a hypothesis test at a 1% level of significance.’’
- The appropriate alternative hypothesis is:
A. Ha: < $145,000.
B. Ha: ≥ $145,000.
C. Ha: > $145,000.
C is the correct answer. I don’t get it.
Ho : When the statement is true
Ha : When the statement is false
thanks for help 
The null hypothesis is the one that you would like to reject.
The general rule in hypothesis testing is to take normal intuition and then reverse it. More often than not, you’ll be o.k.
In other words, you don’t “prove” that house prices are > $145K, you reject that they’re “Not > $145K”. In other words, you “reject the null” that they’re <= $145K.
The Null is what you’re trying to disprove (reject). And the null (at least in the CFA curriculum) contains an = sign:
- In a 2-sided test, you don’t care whether your result is greater than or less than a point (e.g. you want to know if “the return is different from zero”). In that case, the null would be that it’s EQUAL to that point, and the alternate is that it’s UNEQUAL.
- In a one-sided test (like this one), you care if the price is GREATER THAN $145K. So you want to disprove (reject) that it’s less than or equal to $145K. In other words, the null is that the return is LESS THAN OR EQUAL TO $145K.
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